Twinning of isostructural crystals

Hahn, Th.; Klapper, H.

doi:10.1107/97809553602060000644

International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

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International Tables for Crystallography (2006). Vol. D. ch. 3.3, p. 422

Section 3.3.8.6. Twinning of isostructural crystals

Th. Hahn^a ^* and H. Klapper^b

^a Institut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and ^bMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany
Correspondence e-mail: hahn@xtal.rwth-aachen.de

3.3.8.6. Twinning of isostructural crystals

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In the present section, the critical discussion of the lattice theory of twinning is extended from the individual crystal species, treated in Section 3.3.8.5, to the occurrence of merohedral twinning in series of isotypic and homeotypic crystals. The crystals in each series have the same (or closely related) structure, space group, lattice type and lattice coincidences. The following cases are of interest here:

(i) Quartz (SiO₂), quartz-homeotypic gallium phosphate (GaPO₄) and benzil [(C₆H₅CO)₂, so-called `organic quartz'] crystallize under normal conditions in the enantiomorphic space groups and . In quartz, merohedral Dauphiné and Brazil $[\Sigma 1]$ twins are very frequent, whereas twins of the Leydolt (or `combined') law are very rare (cf. Example 3.3.6.3). In gallium phosphate, Leydolt twins occur as frequently as Dauphiné and Brazil twins (Engel et al., 1989). In benzil crystals, however, these twins are never observed, although the same space-group symmetries and conditions for systematic lattice coincidences as in quartz and in gallium phosphate exist. The reason is the completely different structure and chemical bonding of benzil, which is not capable of forming low-energy boundaries for these three twin laws.
(ii) Iron borate FeBO₃, calcite CaCO₃ and sodium nitrate NaNO₃ crystallize under normal conditions in the calcite structure with space group $[R{\bar 3}2/c]$ . The rhombohedral lattice allows twinning with a hexagonal $[\Sigma3]$ coincidence lattice (cf. Example 3.3.6.5). Practically all spontaneously nucleated FeBO₃ crystals grown from vapour (chemical transport) or solution (flux) are $[\Sigma 3]$ -twinned and form intergrowths of reverse and obverse rhombohedra (penetration twins). This kind of twinning is comparatively rare in calcite, where the twins usually appear with another morphology [contact twins on (0001)]. Interestingly, this $[\Sigma3]$ twinning does not occur (or is extremely rare) in sodium nitrate. This shows that even for isotypic crystals, the tendency to form $[\Sigma 3]$ twins is extremely different. This can also be observed for crystals with the sodium chloride structure. Crystals of the silver halogenides AgCl and AgBr, precipitated from aqueous solution, develop multiple $[\Sigma3]$ twins with high frequency (Bögels et al., 1999), and so does galena PbS, whereas the isotypic alkali halogenides (e.g. NaCl, LiF) practically never (or only extremely rarely) form $[\Sigma3]$ twins.
(iii) Another instructive example is provided by the $[\Sigma3]$ (111) spinel twins in the sphalerite (ZnS) structure of III–V and II–VI semiconductor crystals (cf. Example 3.3.6.6). In some of these compounds this kind of twinning is quite rare (e.g. in GaAs), but in others (e.g. InP, CdTe) it is very frequent. Gottschalk et al. (1978) have quantitatively shown that the ease and frequency of twin formation is governed by the (111) stacking-fault energy [which is the energy of the (111) twin boundary ]. They have calculated the (111) stacking-fault energies of various III–V semiconductors, taking into account the different ionicities of the bonds. The results prove quantitatively that the frequency of the $[\Sigma 3]$ twin formation is correlated with the (111) boundary energy.

These examples corroborate the early observations of Cahn (1954, pp. 387–388). The present authors agree with his elegantly formulated conclusion, `that the fact that two substances are isostructural is but a slender guide to a possible similarity in their twinning behaviour'.

References

Bögels, G., Buijnsters, J. G., Verhaegen, S. A. C., Meekes, H., Bennema, P. & Bollen, D. (1999). Morphology and growth mechanism of multiply twinned AgBr and AgCl needle crystals. J. Cryst. Growth, 203, 554–563.Google Scholar

Cahn, R. W. (1954). Twinned crystals. Adv. Phys. 3, 202–445.Google Scholar

Engel, G., Klapper, H., Krempl, P. & Mang, H. (1989). Growth twinning in quartz-homeotypic gallium orthophosphate crystals. J. Cryst. Growth, 94, 597–606.Google Scholar

Gottschalk, H., Patzer, G. & Alexander, H. (1978). Stacking fault energy and ionicity of cubic III–V compounds. Phys. Status Solidi A, 45, 207–217.Google Scholar

International Tables for Crystallography (2006). Vol. D. ch. 3.3, p. 422